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Game Theory: Decisions, Interaction and Evolution (Springer Undergraduate Mathematics Series) Paperback – December 1, 2006


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Game Theory: Decisions, Interaction and Evolution (Springer Undergraduate Mathematics Series) + An Introductory Course on Mathematical Game Theory (Graduate Studies in Mathematics)
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Product Details

  • Series: Springer Undergraduate Mathematics Series
  • Paperback: 242 pages
  • Publisher: Springer; 2007 edition (December 1, 2006)
  • Language: English
  • ISBN-10: 1846284236
  • ISBN-13: 978-1846284236
  • Product Dimensions: 0.4 x 7.1 x 9.2 inches
  • Shipping Weight: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,750,673 in Books (See Top 100 in Books)

Editorial Reviews

Review

From the reviews:

“This is supposed to be a mathematical introduction to game theory for undergraduate students. I think both students of economics and mathematics (both with a course of calculus, linear algebra and optimization in Rn) can use this book. The idea of the book is to provide the ‘intuition’ behind some important theorems of game theory.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, March, 2014)

"A single-semester elective course in game theory would be an attractive feature of any undergraduate mathematics program. Students would get to use the various mathematical skills they have acquired in a thought-provoking applied context. The book under review is intended as a textbook for such a course. … Certainly the choice of topics and overall organization is good." (David P. Roberts, MathDL, August, 2007)

From the Back Cover

This introduction to game theory is written from a mathematical perspective. Its primary purpose is to be a first course for undergraduate students of mathematics, but it also contains material which will be of interest to advanced students or researchers in biology and economics.

The outstanding feature of the book is that it provides a unified account of three types of decision problem:

  • Situations involving a single decision-maker: in which a sequence of choices is to be made in "a game against nature". This introduces the basic ideas of optimality and decision processes.
  • Classical game theory: in which the interactions of two or more decision-makers are considered. This leads to the concept of the Nash equilibrium.
  • Evolutionary game theory: in which the changing structure of a population of interacting decision makers is considered. This leads to the ideas of evolutionarily stable strategies and replicator dynamics.

An understanding of basic calculus and probability is assumed but no prior knowledge of game theory is required. Detailed solutions are provided for the numerous exercises.


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2 of 2 people found the following review helpful By Daniel O. Cajueiro on February 15, 2011
Format: Paperback Verified Purchase
This is supposed to be a mathematical introduction to game theory for undergraduate students. I think both students of economics and mathematics (both with a course of calculus, linear algebra and optimization in Rn) can use this book. The idea of the book is to provide the "intuition" behind some important theorems of game theory. For instance, in order to prove that every game has a Nash equilibrium, instead of using the Kakutani fixed point theorem, it proves the simpler statement "Every two player, two action game has at least one Nash equilibrium", without the fixed point theorem. An interesting aspect of this book is the fact that it also has an introduction to Evolutionary Game Theory. If you are not necessarily interested in the proofs, there are more intuitive introductions. I strongly suggest Game Theory for Applied Economists by Robert Gibbons or Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction by Herbert Gintis.
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1 of 1 people found the following review helpful By W Boudville HALL OF FAMETOP 1000 REVIEWERVINE VOICE on November 21, 2007
Format: Paperback
Webb's treatment of game theory is directed at experienced mathematicians. You need a solid background in probability and statistics. Including covering Markov processes. The reason for the latter is that repeated games are discussed in the text. Often, the modelling of these involving using Markov decision processes.

If you have already read some introductory texts on game theory, including perhaps the classic early one by Neumann and Morganstern (1953), then Webb's book will likely present a more rigorous and comprehensive treatment.

Of interest is also the chapters on evolutionary games. Where success is defined in terms of reproduction.
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Format: Paperback Verified Purchase
This book includes several applications about the stochastics aspects of the game theory. In fact the author analyzes particularly the Markov chains method. Next he consider the Nash bargaining and other aspects as the traditional arguments of the duopoly and the subgames.The more immediate applications are about the population theory, that usually is considerated part of the biology.
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